Question

A long Straight wire carries 5A along a positive x axis and a second wire carries 7A along positive y axis find their combine field at the point x=4cm and Y=6cm

Answer 1

$B = \frac{\mu_0I}{2\pi R}$

$\mu_0\approx1.2567*10^{-6}\frac{H}{m}$

$B_x = \frac{\mu_0I_x}{2\pi R_x}$

$I_x= 5A$

$R_x= 6cm =0.06m \text{ distance to the X-axis}$

$B_x = \frac{\mu_0*5}{2\pi *0.06}\approx1.67*10^{-5}T$

$B_y = \frac{\mu_0I_y}{2\pi R_y}$

$I_y= 7A$

$R_y= 4cm =0.04m \text{ distance to the Y-axis}$

$B_y = \frac{\mu_0*7}{2\pi *0.04}\approx3.5*10^{-5}T$

$\text{since the axes X ,Y are perpendicular}$

$B =\sqrt{B_x^2+B_y^2}= 10^{-5}\sqrt{1.67^2+3.5^2}\approx3.88*10^{-5}T$

$\text{Answer:}B =3.88*10^{-5}T$